Friday, June 22, 2012

Arnold Sommerfeld: Father of Quantum Physicists

Arnold Sommerfeld
(1868-1951)

Arnold Sommerfeld is a man that I had not heard of until taking a course in solid state physics. And I apologize to those of you who may hear the name with dread, but despite creating the Sommerfeld Equation, he really is an interesting guy, so please stick with me. And I will only mention the Sommerfeld Equation one more time. While he appears to have been known in his own time as a great mathematician and physicist, he is even better known by the students that he advised. These include Werner Heisenberg, Wolfgang Pauli, Peter Debye, and Alfred Landé, among many others. And these are just the students considered to be his advisees by the mathematics genealogy project. Others famous men who studied with Sommerfeld include Linus Pauling, Léon Brillouin, and Rudolf Peierls. He also has the unfortunate honor of being the man between 1901 and 1950 to receive the most nominations for a Nobel Prize without actually winning one, receiving eighty-one nominations.

Arnold Sommerfeld was born in 1868 in Germany, and studied mathematics and natural science at the University of Köningsberg, receiving his PhD in 1891. He was an assistant professor at the University of Göttingen in mathematics and in mineralogy, before becoming a professor of mathematics at the Mining Academy of Claustel and then a professor of mechanics at the Institute of Technology of Aachen. In 1906 he become the head of the Department of Theoretical Physics at the University of Munich, a position that had previously been held by Ludwig Boltzmann. The University of Munich was well known in the field of theoretical physics, so this was both a great honor and a wonderful opportunity for Sommerfeld to influence a new generation of physicists. He taught there from 1906 to 1935, when he retired.

When he receive the post of chair of Theoretical Physics, Sommerfeld wanted to learn more about the field, since he himself was a mathematician, not a physicist. He asked Abraham Joffe, who had helped to discover x-rays, for help in understanding physics. He suggested that they meet every morning at a café to discuss experimental physics, and these discussions quickly included many more scholars eager to discuss new ideas. Apparently he was a great lecturer, and was able to explain the complexities of atomic structure and other confusing topics with great clarity.

His research started out in the field of the propagation of radio waves, which now seems rather outdated, but at that time was of vital importance. The telephone had been developed in the late nineteenth century, but by 1900, most people conveyed important communications by telegraph. While telegraphs traveled by wires in many parts of the country, telegraphs to ships required radio waves, and the difficulties with sustaining a cable across the Atlantic meant that transatlantic communications would have to be by radio waves. The first wireless telegraph was patented in 1897 by Guglielmo Marconi (who shared the Nobel Prize in physics in 1909 for his work with wireless telegraphy), and the first transatlantic telegraphic communications via radio waves were accomplished in 1901. Sommerfeld's 1909 paper "The Propagation of Waves in Wireless Telegraphy" was thus of vital importance at the time, and has been oft cited.

As well as working with radio waves, Sommerfeld also worked with x-rays, still a very new and mysterious phenomenon, and his student Max von Laue showed that x-rays are also an electromagnetic wave (and won a Nobel Prize for it). Sommerfeld went on to develop the relativistic quantum theory of the fine structure of the hydrogen spectrum. Quantum theory is difficult enough, but adding relativity is quite an accomplishment. I first met the name Sommerfeld when considering the electronic theory of metals, where he developed the Sommerfeld Equation as a method to approximate functions as a function of temperature. He is also famous for his work with atomic theory and atomic physics, in the end publishing a six volume series on the subject of theoretical physics and going on two lecture tours in the United States. Unfortunately, however, he met his death as a result of an automobile accident in 1951. As Linus Pauling wrote, "The hazard of a mechanized world has prevented his students from celebrating during his lifetime still further anniversaries of the birth of this great man."